Rational Exponents and Radicals

a

We start by rewriting the radical expressions as rational exponents. Then, you use the properties of exponents to simplify the expression.

7 \cdot 7 \cdot 7

a = a^{\frac{1}{2}}

7^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} \cdot 7^{\frac{1}{2}}

a^{m} \cdot a^{n} = a^{m + n}

7^{\frac{1}{2} + \frac{1}{2} + \frac{1}{2}}

AddFracAdd fractions

7^{\frac{3}{2}}

The expression can be written as $7^{\frac{3}{2}} .$

b

We solve this exercise just like we did in Part A. However, this time we have cube roots instead of square roots.

35 \cdot 35

n a = a^{\frac{1}{n}}

5^{\frac{1}{3}} \cdot 5^{\frac{1}{3}}

a^{m} \cdot a^{n} = a^{m + n}

5^{\frac{1}{3} + \frac{1}{3}}

AddFracAdd fractions

5^{\frac{2}{3}}

We therefore get $5^{\frac{2}{3}} .$

Rational Exponents and Radicals 1.20 - Solution